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AO and KI meet on $\Gamma$

Source: Indian TST 3 P2

July 17, 2019
anant mudgal geogeometryHi

Problem Statement

Let ABCABC be an acute-angled scalene triangle with circumcircle Γ\Gamma and circumcenter OO. Suppose AB<ACAB < AC. Let HH be the orthocenter and II be the incenter of triangle ABCABC. Let FF be the midpoint of the arc BCBC of the circumcircle of triangle BHCBHC, containing HH.
Let XX be a point on the arc ABAB of Γ\Gamma not containing CC, such that ∠AXH=∠AFH\angle AXH = \angle AFH. Let KK be the circumcenter of triangle XIAXIA. Prove that the lines AOAO and KIKI meet on Γ\Gamma. Proposed by Anant Mudgal
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